Divide the polynomials.
Solution: Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. $\begin{array}{r} x+2 \\ x+3|\overline{x^2+5x+5} \\ \mathllap{-(}\underline{x^2+3x\phantom{+5}\rlap )} \\ 2x+5 \\ \mathllap{-(}\underline{2x+6\rlap )} \\ -1 \end{array}$ We get that the quotient is $x+2$ and the remainder is $-1$, and therefore: $\dfrac{x^2+5x+5}{x+3}=x+2-\dfrac{1}{x+3}$ [I want to see a different way of performing the division.]